The socially stable core in structured transferable utility games
This discussion paper resulted in a publication in 'Games and Economic Behavior', 2007, 59, 85-104. We consider cooperative games with transferable utility (TU-games), in which we allow for a social structure on the set of players. The social structure is utilized to refine the core of the game. For every coalition the relative strength of a player within that coalition is induced by the social structure and is measured by a power function. We call a payoff vector socially stable if at the collection of coalitions that can attain it, all players have the same power. The socially stable core is the set of socially stable elements of the core. We show that the socially stable core is non-empty if the game itself is socially stable. In general the socially stable core consists of a finite number of faces of the core and generically consists of a finite number of payoff vectors. Convex TU-games have a non-empty socially stable core, irrespective of the power function. When there is a clear hierarchy of players in terms of power, the socially stable core of a convex TU-game consists of exactly one element, an appropriately defined marginal vector. We demonstrate the usefulness of the concept of the socially stable core by two applications. One application concerns sequencing games and the other one the distribution of water.
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- Herings,P. Jean-Jacques & Laan, van der,Gerard & Talman,Dolf, 2003.
"Socially Structured Games and Their Applications,"
024, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Le Breton,Michel & Owen,Guillermo & Weber,Shlomo, 1991.
"Strongly balanced cooperative games,"
Discussion Paper Serie A
338, University of Bonn, Germany.
- P. Herings & Gerard Laan & Dolf Talman, 2005. "The positional power of nodes in digraphs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(3), pages 439-454, 06.
- AMBEC, Steve & SPRUMONT, Yves, 2000.
"Sharing a River,"
Cahiers de recherche
2000-08, Universite de Montreal, Departement de sciences economiques.
- Ambec, S. & Sprumont, Y., 2000. "Sharing a River," Cahiers de recherche 2000-08, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Ambec, Stefan & Sprumont, Yves, 2000. "Sharing a River," Cahiers de recherche 0006, GREEN.
- Ambec, S. & Sprumont, Y., 2000. "Sharing a River," Papers 00-06, Laval - Recherche en Energie.
- Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
- Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 227-240.
- Matthew O. Jackson & Asher Wolinsky, 1994.
"A Strategic Model of Social and Economic Networks,"
1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Gilles, R.P. & Owen, G. & van den Brink, J.R., 1991.
"Games with permission structures : The conjunctive approach,"
FEW 473, Tilburg University, School of Economics and Management.
- Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
- Gilles, R.P. & Owen, G. & van den Brink, J.R., 1991. "Games with permission structures : The conjunctive approach," Discussion Paper 1991-14, Tilburg University, Center for Economic Research.
- Kalai, Ehud & Postlewaite, Andrew & Roberts, John, 1978. "Barriers to trade and disadvantageous middlemen: Nonmonotonicity of the core," Journal of Economic Theory, Elsevier, vol. 19(1), pages 200-209, October.
- Gabrielle Demange, 1994.
"Intermediate Preferences and Stable Coalition Structures,"
- Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
- Demange, G., 1991. "Intermediate Preferences and Stable Coalition Structures," DELTA Working Papers 91-16, DELTA (Ecole normale supérieure).
- Gabrielle Demange, 2004.
"On Group Stability in Hierarchies and Networks,"
Journal of Political Economy,
University of Chicago Press, vol. 112(4), pages 754-778, August.
- Kaneko, Mamoru & Wooders, Myrna Holtz, 1982.
"Cores of partitioning games,"
Mathematical Social Sciences,
Elsevier, vol. 3(4), pages 313-327, December.
- van den Brink, J.R. & Gilles, R.P., 1991.
"Axiomatizations of the conjunctive permission value for games with permission structures,"
FEW 485, Tilburg University, School of Economics and Management.
- van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
- Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
- Hamers, H.J.M., 1995. "Sequencing and delivery situations : A game theoretic approach," Other publications TiSEM f2cbf2cf-aa4e-4f9d-b46d-7, Tilburg University, School of Economics and Management.
- Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 249-266.
- Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
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